Mr Trump raised the idea at a private meeting with NATO leaders in Brussels, White House press secretary Sarah Huckabee Sanders confirmed.
No deadline for the increase has been mentioned.
Mr Trump has been pressing member countries to spend more on defence, accusing them of passing the burden on to the US.
NATO estimates that 15 members, or just over half, will meet the benchmark of 2% by 2024 based on current trends.
Tweeting after a day of meetings on Wednesday, Mr Trump called on member nations to immediately boost spending.
He said: “Why are their (sic) only 5 out of 29 countries that have met their commitment? The U.S. is paying for Europe’s protection, then loses billions on Trade. Must pay 2% of GDP IMMEDIATELY, not by 2025.”
NATO nations have already committed to spending at least 2% of GDP on defence by 2024.
Around eight members of the 29-country alliance are expected to reach the 2% target this year.
Asked about Mr Trump’s suggestion, NATO Secretary-General Jens Stoltenberg said he would focus on what has been agreed to.
“We have agreed that we’re committed to the pledge increasing defense spending to 2%. So let’s start with that,” he said.
Speaking after what he called a “substantive meeting”, Mr Stoltenberg acknowledged the day’s conversations had included “disagreements”.
Mr Stoltenberg detailed some of the agreements settled on Wednesday, including:
:: Providing training to Iraqi troops and supporting Jordan and Tunisia in battling terrorism
:: By 2020, it was agreed 30 additional mechanised battalions, air squadrons and combat vessels should to be ready to be deployed within 30 days or less.
:: An update to the NATO command structure and more resource for NATO allies on areas such as cybercrime and energy security.
Mr Trump earlier claimed that Germany was “captive to Russia”.
“Germany, as far as I’m concerned, is captive of Russia because it is getting so much of its energy from Russia,” he said.
German Chancellor Angela Merkel later responded defiantly, saying: “I’ve experienced myself a part of Germany controlled by the Soviet Union and I’m very happy today that we are united in freedom as the Federal Republic of Germany and can thus say that we can determine our own policies and make our own decisions and that’s very good.”